Let \(\mathcal {X}\)  be the set of all face-edge paths \(\pi \)  such that \(\phi (\pi )\notin \Gamma (\pi )\) .
Note that, if \(\pi \in \mathcal {X}\) , then \(\pi ^{-1}\in \mathcal {X}\) .
We compute \(\bar{f}_\pi \)  for each pair \(\pi \in \mathcal {X}\) , and check
if \(\pi \)  and \(\pi ^{\prime }\)  are co-viable for each pair \((\pi ,\pi ^{\prime })\)  of face-edge paths in \(\mathcal {X}\) .
Then, we find a set \(X\subset \mathcal {X}\)  such that (i) For each path \(\pi \)  of \(\mathcal {X}\) , \(X\)  contains at least one of \(\pi \)  or \(\pi ^{-1}\) , (ii) every pair of face-edge paths in \(X\)  is co-viable.
Then we return \(\bigvee _{\pi \in X} \bar{f}_\pi \) . For its correctness, refer to [1]}.
